Cremona's table of elliptic curves

6489 = 3² · 7 · 103

Field	Data	Notes
Atkin-Lehner	3- 7+ 103-	Signs for the Atkin-Lehner involutions
Class	6489c	Isogeny class
Conductor	6489	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	8448	Modular degree for the optimal curve
Δ	-79505194167 = -1 · 38 · 76 · 103	Discriminant
Eigenvalues	1 3-  4 7+  2 -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-855,16848]	[a1,a2,a3,a4,a6]
Generators	[-2880:20772:125]	Generators of the group modulo torsion
j	-94881210481/109060623	j-invariant
L	5.9241799783936	L(r)(E,1)/r!
Ω	0.98298316814307	Real period
R	6.0267359303668	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	103824ch1 2163a1 45423i1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 6489c1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
1	-	4	+	2	-2	-6	4	-4	-10	-4	-10	-2	-2	8	14	-4	-14	-10	-10	0	0	-4	0	2

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Quadratic twists for elliptic curve 6489c1

-4	-3	-7
103824ch1	2163a1	45423i1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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